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Zap. Nauchn. Sem. POMI, 2013, Volume 415, Pages 62–74 (Mi znsl5686)  

Groups acting on dendrons

A. V. Malyutin

St. Petersburg Department of Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia

Abstract: A dendron is a continuum (a non-empty connected compact Hausdorff space) in which every two distinct points have a separation point. We prove that if a group $G$ acts on a dendron $D$ by homeomorphisms, then either $D$ contains a $G$-invariant subset consisting of one or two points, or $G$ contains a free non-commutative subgroup and, furthermore, the action is strongly proximal.

Key words and phrases: dendron, dendrite, tree, $\mathbb R$-tree, pretree, dendritic space, amenability, invariant measure, von Neumann conjecture, Tits alternative, free non-Abelian subgroup, strong proximality.

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English version:
Journal of Mathematical Sciences (New York), 2016, 212:5, 558–565

UDC: 512.54+515.12
Received: 06.05.2013

Citation: A. V. Malyutin, “Groups acting on dendrons”, Geometry and topology. Part 12, Zap. Nauchn. Sem. POMI, 415, POMI, St. Petersburg, 2013, 62–74; J. Math. Sci. (N. Y.), 212:5 (2016), 558–565

Citation in format AMSBIB
\Bibitem{Mal13}
\by A.~V.~Malyutin
\paper Groups acting on dendrons
\inbook Geometry and topology. Part~12
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 415
\pages 62--74
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5686}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 212
\issue 5
\pages 558--565
\crossref{https://doi.org/10.1007/s10958-016-2688-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84953410388}


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